Effects of grid straggering on numerical schemes. (English) Zbl 0661.76024
Nine finite difference schemes using primitive variables on various grid arrangements were systematically tested on a benchmark problem of two- dimensional incompressible Navier-Stokes flows. The chosen problem is similar to the classical lid-driven cavity flow, but has a known exact solution. Also, it offers the reader an opportunity to thoroughly evaluate accuracies of viscous conceptual grid arrangements. Compared to the exact solution, the non-staggered grid scheme with higher-order accuracy was found to yield an accuracy significantly better than others. In terms of ‘overall performance’, the so-called 4/1 staggered grid scheme proved to be the best. The simplicity of this scheme is the primary benefit. Furthermore, the scheme can be changed into a non- staggered grid if the pressure is replaced by the pressure gradient as a field variable.
Finally, the conventional staggered grid scheme developed by F. H. Harlow and F. E. Welch [Phys. Fluids 8, 2182-2189 (1965)] also yields relatively high accuracy and demonstrates satisfactory overall performance.
Finally, the conventional staggered grid scheme developed by F. H. Harlow and F. E. Welch [Phys. Fluids 8, 2182-2189 (1965)] also yields relatively high accuracy and demonstrates satisfactory overall performance.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M99 | Basic methods in fluid mechanics |
| 65N22 | Numerical solution of discretized equations for boundary value problems involving PDEs |
Keywords:
finite difference schemes; benchmark problem; two-dimensional incompressible Navier-Stokes flows; classical lid-driven cavity flowReferences:
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